On the other hand, next we fix the grid aspect ratio and vary the Reynolds number. Figures REF  and REF  present the velocity profiles along the vertical and horizontal centerlines obtained using RNR-LBM and RC-LBM, respectively, with \(a=0.5\)  at \(\mbox{Re} = 100, 1000, 3200, 5000\)  and 7500. The computed results again match well with those provided in Ref. [1]} for all the \(\mbox{Re}\)  tested. By contrast, it may be noted that Ref. [2]} reported that the use of a prior rectangular MRT-LB scheme [3]} became unstable for \(\mbox{Re}>1000\) , while the more recent rectangular MRT-LB formulations showed results for \(\mbox{Re}=100\)  in Ref. [4]} and up to \(\mbox{Re=3200}\)  in Ref. [2]}. All these prior schemes used orthogonal moment basis. Furthermore, a more recent rectangular SRT-LBM also showed results only up to \(\mbox{Re}=1000\)  [6]}. On the other hand, our RNR-LBM and RC-LBM can reach significantly higher values of \(\mbox{Re}\) , including 7500, the largest value for which the benchmark data involving steady state results for making comparisons are available [1]}. Moreover, in the next section involving a numerical stability study, simulations with even higher Reynolds numbers will be reported.
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